Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
Quantum computation and quantum information
Quantum computation and quantum information
Classical and Quantum Computation
Classical and Quantum Computation
Geometry of Interaction and linear combinatory algebras
Mathematical Structures in Computer Science
A Lambda Calculus for Quantum Computation
SIAM Journal on Computing
Time, space, and energy in reversible computing
Proceedings of the 2nd conference on Computing frontiers
Probabilistic λ-calculus and Quantitative Program Analysis
Journal of Logic and Computation
A reversible programming language and its invertible self-interpreter
Proceedings of the 2007 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
Reversible Computation and Reversible Programming Languages
Electronic Notes in Theoretical Computer Science (ENTCS)
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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The $\lambda$-calculus is destructive: its main computational mechanism, beta reduction, destroys the redex, which makes replaying the computational steps impossible. Combinatory logic is a variant of the $\lambda$-calculus that maintains irreversibility. Recently, reversible computational models have been studied mainly in the context of quantum computation, as (without measurements) quantum physics is inherently reversible. However, reversibility also fundamentally changes the semantical framework in which classical computation has to be investigated. We describe an implementation of classical combinatory logic in a reversible calculus for which we present an algebraic model based on a generalisation of the notion of a group.